Malcolm Turnbull announced the decision on Friday.

Former Prime Minister Kevin Rudd has released a series of letters which he claims shows Malcolm Turnbull was planning to back him for the role of UN Secretary-General.

Sky News reports that in the letters Rudd said he had numerous assurances from the current PM supporting his tilt for the prestigious role as late as December.

"You will recall that last September I contacted you asking for guidance on how I should address the matter of your previously stated support to me for my candidature when I met Foreign Minister Bishop at the UN General Assembly," he writes.

"You in fact sent me a message on your preferred Wickr system where you stated that you and the FM were 'as one' in your support for my candidature."

My thanks also to Australian Foreign Minister Bishop and her ministerial colleagues for their support for UNSG. Unfortunately PM disagreed.

"I do not want to add to his disappointment, but the threshold point here is when the Australian Government nominates a person for a job, particularly an international job like this, the threshold question is: Do we believe the person, the nominee, the would-be nominee is well suited for that position?" Turnbull said at a press conference on Friday.

"My judgement is that Mr Rudd is not, and I've explained to him the reasons why. I don't want to go into them here today."

Turnbull denied that the decision was based on the fact that Rudd was a former Labor politician.

"I can assure you that this is not a partisan issue. This is a considered judgement about Mr Rudd's suitability for the role in question, that is to say Secretary-General of the United Nations," he said.

"Not everyone is well suited for every role. This is no disparagement of Mr Rudd. He is a former prime minister of Australia. But my judgement is that he is not well suited for this particular role."

"It is a pity the Government has not seen fit to support him, as the Hawke Government supported Malcolm Fraser for the post of Secretary General of the Commonwealth, or the Howard Government supported Gareth Evans to be head of UNESCO," the statement read.

Rudd took a subtle dig at Turnbull for the way the decision was relayed.

"Mr Rudd flew to Sydney this morning requesting a meeting with the Prime Minister, having sought such a meeting the previous evening. On arrival in Sydney Mr Turnbull telephoned Mr Rudd, indicating there was no opportunity for a meeting," the statement read.

"Mr Rudd thanks Foreign Minister Bishop, and her many Cabinet colleagues for their consideration of and support for his candidacy for United Nations Secretary General. It would have been the first time in the United Nation's 70 year history that Australia offered a candidate for UN Secretary General."

"It would have reflected well on what our nation can offer to the world - as a middle power with relationships across the world, including the developing world, smaller states, the Commonwealth, our Pacific Island friends and of course our partners in Asia."

Rudd has issued a statement re Secretary General snub: "It is a pity the Government has not seen fit to support him" pic.twitter.com/YNVnAA5imw

The Australian reported strong opposition to nominating Rudd from the cabinet, after senior figures including Scott Morrison and Peter Dutton had publicly criticised Rudd's suitability for the U.N. job. Labor politicians, on the other hand, had strongly backed Rudd's bid, with the likes of Anthony Albanese, Tanya Plibersek and Chris Bowen pushing his case.